Parity anomalies in 2+1-dimensional Aharonov-Bohm type configurations

TL;DR

This paper reveals that Dirac fermions in 2+1 dimensions coupled to gauge fields exhibit a parity anomaly manifesting as Aharonov-Bohm and Aharonov-Casher phases, with explicit calculations of topological currents.

Contribution

It demonstrates the existence of a parity anomaly in 2+1D Dirac fermions leading to topological phases and calculates associated currents using the Fujikawa method.

Findings

Parity anomaly causes Aharonov-Bohm and Aharonov-Casher phases.

Induced topological currents are divergence-free.

Explicit calculation confirms the anomaly's physical effects.

Abstract

We demonstrate that Dirac fermions in 2+1 dimensions, coupled to Abelian gauge fields in multiply-connected regions, exhibit a parity anomaly that directly manifests as Aharonov-Bohm (AB) type topological phases. Using the Fujikawa method, we show that this anomaly reproduces both the AB phase and the spin-dependent Aharonov-Casher (AC) phase. We explicitly calculate the induced topological currents, establishing that their characteristic divergence-free form provides a direct signature of this parity-anomalous topological phase.